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Review Automatic Control

Review Automatic Control. Instructor: Cailian Chen, Associate Professor Department of Automation. 27 December 2012. Structure of the course. Linear Time-invariant System (LTI). Analysis. Time Domain Complex Domain Frequency Domain. System Model. Concepts. Performance.

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Review Automatic Control

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  1. ReviewAutomatic Control Instructor: Cailian Chen, Associate Professor Department of Automation 27 December 2012

  2. Structure of the course Linear Time-invariant System (LTI) Analysis Time Domain Complex Domain Frequency Domain System Model Concepts Performance Compensation Design 各章概念融会贯通 解题方法灵活运用

  3. Time Constant Canonical Form (Bode Form) ； Root Locus Canonical Form (Evan’s Form) ；

  4. j [S plane] Stable Region Unstable Region  0 Stability Analysis Method (1) RouthFormula (2) Root Locus Method (3) Nyquist Stability Criterion Z＝N＋P Stability: All of the roots of characteristic equation of the closed-loop system locate on the left-hand half side of s plane.

  5. Summary of Chapter 5 • Understand and remember of root locus equation • Rules for sketching of root locus • Calculate Kg andK by using magnitude equation

  6. R(s) + E(S) C(s) G(s) Magnitude equation - Phase equation Argument equation H(s) Characteristic equation of the closed-loop system 2019/12/20 6

  7. Rules for Plotting Root Locus

  8. Important rules Rule 4: Segments of the real axis Rule 5: Asymptotes of locus as s Approaches infinity Rule 6: Breakaway and Break-in Points on the Real Axis Rule 7: The point where the locus crosses the imaginary axis substituting s=jωinto the characteristic equation and solving for ω； Use Routh Formula 2019/12/20 9

  9. Summary of Chapter 6 • Complete Nyquist Diagram • Bode Diagram • NyquistStability Criterion • Relative Stability

  10. Open-loop transfer function with integration elements Type I system（ν＝1） Type II system (ν = 2)

  11. Type II open-loop system with inertial elements Type I open-loop system only with inertial elements Intercept with real axis is most important, and can be determined by the following method: A. Solve Im[G(jω)]=0 to get ω and then get Re[G(jω)]； B. Solve ∠G(jω) = k·180°(kis an integer)

  12. Draw the complete Nyquist Diagram (ω)：＋90ν°→ 0°→－90ν°

  13. Bode Diagram: Always Use Asymptotes • Change the open-loop transfer function into the Bode Canonical form • The slope of lower frequency line is －20νdB/dec，where ν is the type of open-loop system. For ω＝1, L(1)=201gK • If there exist any break frequency less than 1, the point with ω＝1 and L(1)=201gK is on the extending lineof lower frequency line.

  14. Nyquist stability criterion • If N≠－P，the closed-loop system is unstable. The number of poles in the right-hand half s plane of closed-loop system is Z＝N＋P. • If the open-loop system is stable，i.e. P=0，then the condition for the stability of closed-loop system is: the complete Nyquist diagram does not encircle the point (－1, j0), i.e.N=0.

  15. Relative Stability • Phase margin γ 2. Gain margin γ

  16. 相角裕度和增益裕度

  17. Summary of Chapter 7 • Phase Lead Compensation Multiplying the transfer function by α 2019/12/20 18

  18. Rules to design phase lead compensation • (1) Determine K to satisfy steady-state error constraint (2) Determine the uncompensated phase margin γ0 (3) estimate the phase margin in order to satisfy the transient response performance constraint (4) Determine Extra margin: 5o~10o (5) Calculate ωm (6) DetermineT (7) Confirmation

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